Calculus I - Spring 2008

Instructor:
**S. M. Mintchev**

Locations:
**Mon - Rm. 521; Th - Rm. 315; Fri - Rm. 143
**

Instructor Information:

- email address:
**mintchev@cims.nyu.edu** -
office: Cooper Union - Engineering Bldg., Rm. 460

**; also at Warren Weaver Hall (NYU), Rm. 718** -
telephone:

**212-998-3107** - office hours: Tue 2:00pm-4:00pm; Th 5:00pm-6:00pm

Text: Calculus and Analytic Geometry. Stein, Sherman K. and Barcellos, Anthony. Fifth edition. McGraw-Hill, 1992.

Grading Policy: There will be six homework assignments
collected throughout the semester. This page will contain a posting of
required and suggested homework exercises from each section covered.
Required problems are marked with an asterisk. In
addition to these assigments there will be two
exams during the semester; the exams will be administered at the one
third, resp. two thirds, marks of the semester. The first exam will
cover the first third of the material; the second will cover the second
third. There will be a final examination administered on the last day
of class; this exam will cover all of the material taught in the
course. The
values of these components
towards the final grade in the course are
presented below:

Component |
Value |

Homework |
20 % |

Exam 1 |
25 % |

Exam 2 |
25 % |

Final Exam |
30 % |

Syllabus (please
note that this schedule is tentative and will
likely be adjusted as the semester progresses):

Date |
Chapter.Section |
Topic |

01/24/2008 |
I |
Introduction
and Notation, Course Information |

01/25/2008 | 2.1, 2.2 | Review of Real Number System and Functions |

01/28/2008 | 2.3, 2.4,
2.10 |
Definition
of Limit, Computations |

01/31/2008 | 2.4, 2.8, 2.9 |
Continuity,
More Computations of Limits |

02/01/2008 | 2.6, 2.7 |
Trigonometric
Limits |

02/04/2008 | 3.1, 3.2 |
The
Derivative |

02/07/2008 | 3.3, 3.4 |
Derivative
& Continuity; Rules For Differentiation |

02/08/2008 | 3.5, 3.6 |
Derivatives
of Trigonometric Functions; Chain Rule Homework 1 DUE |

02/11/2008 | 4.1, 4.2 |
Rolle's
Theorem & Mean-Value Theorem; Graphing |

02/14/2008 | 4.3 |
Second
Derivative; Kinematics |

02/15/2008 | 4.4, 4.5 |
Related
Rates; Graphing |

02/21/2008 | 4.6, |
Newton's
Method; |

02/22/2008 | 4.7, 4.8 |
Optimization;
Implicit Differentiation; |

02/25/2008 | 4.9, 4.10 |
Linear
Approximation; Growth Estimates Homework 2 DUE |

02/28/2008 | REVIEW |
Review for
Exam 1 |

02/29/2008 | EXAM 1 |
Sections
2.1-4.8 |

03/03/2008 | Graphing
Workshop |
A
Review of Graphing Tools; Examples |

03/06/2008 | Exam
1; 5.1 |
Area
Estimates |

03/07/2008 | 5.2-5.4 |
Summation
Notation, Definite Integral, Estimations |

03/10/2008 | 5.5,5.6 |
Antiderivatives,
Intro to Fundamental Theorem |

03/13/2008 | 5.7 |
Fundamental
Theorem of Calculus |

03/14/2008 | 6.1,6.2 |
The
Logarithm and Natural Number e Homework 3 + Graphing Worksheet DUE |

03/24/2008 | 6.3,6.4 |
Derivatives
of Logarithmic Functions |

03/27/2008 | 6.5 |
Derivatives
of Exponential Functions |

03/28/2008 | 6.6,6.7 |
Derivatives
of Inverse Trig, Natural Growth/Decay |

03/31/2008 | 6.8,6.9 |
L'Hopital's
Rule; Hyperbolic Functions |

04/03/2008 | REVIEW |
Review
for Exam 2 |

04/04/2008 | EXAM 2 |
Sections
4.9-6.7; Graphing Homework 4 DUE |

04/07/2008 | Workshop:
7.1 |
Integration with Integral Tables |

04/10/2008 | Workshop: 7.2 | Integration
by Substitution |

04/11/2008 | Workshop: 7.3 | Integration by Parts |

04/14/2008 | Workshop |
Special Techniques for Integrals of Trig Functions |

04/17/2008 | Workshop: 7.4 | Integration
of Rational Functions |

04/18/2008 | Workshop: 7.5 | Method
of Partial Fractions |

04/21/2008 | Workshop: | Some
Special Methods: Rational fns. of sine and cosine |

04/24/2008 | Workshop: 7.6 | Special
Substitutions |

04/25/2008 | Workshop: 7.7 | Work
on Integration (students at Blackboard) Homework 5 DUE |

04/28/2008 | Workshop | Final Review Exercises (students at Blackboard) |

05/01/2008 | Workshop | Final Review Exercises (students at Blackboard) |

05/02/2008 | Workshop | Final Review Exercises (students at Blackboard) |

05/05/2008 | Workshop | Final Review Exercises (students at Blackboard) |

05/08/2008 | Workshop | Final Review Exercises (students at Blackboard) |

05/09/2008 | Workshop | Final
Review Exercises (students at Blackboard) Homework 6 DUE |

05/12/2008 | FINAL EXAM |
Cumulative
(covers entire course) |

Homework Assigments
(please see grading policy section for requirements):

* - submission of problem required for grading

Section |
Problem |

2.1 | 17,21*,22,23,27*,28*,41,44,(46-53)* |

2.2 |
19,22,24,26,29*,30*,31,32*,33,34,35,36* |

2.3 |
2*,4,6*,8,10,12*,13*,14*,16,20,22*,27,28,29,30* |

2.4 |
4,10,17*,20,22*,33*,39*,46* |

2.5 |
3,4,5*,29-31,32*,35*,36*,41*,42,43,44 |

2.6 |
43*,51,52*,53*,54*,56 |

2.7 |
(3-10)*,15,16*,28* |

2.8 |
1-10,12*,16*,26*,37,39*,40* |

3.1 |
6*,9,18* |

3.2 |
11,14,16,
25*, 28*, 38*, 40* |

3.3 |
1, 3, 9,
(15-18)*, (26-28)* |

3.4 |
14, 18*, 24,
28, 34*, 35*, 38*, (47-48)* |

3.5 |
19-21,
(22-24)*,
34*, 44* |

3.6 |
19*, 20*,
(28-30)*, 37*, 38*, 54* |

4.1 |
8, 10*, 18*,
26*, 46* |

4.2 |
8*, (9-16)*,
44, 48* |

4.3 |
23, 26, 28* |

4.4 |
4, 5, 10,
17*, 23* |

4.5 |
11, 14, 16*,
24*, 25, 35*, 40*, 41 |

4.6 |
19, 26, 28 |

4.7 |
8*, 11, 12,
16, 25*, 30*, 37, 39, 46*, 50* |

4.8 |
3*, 20* |

4.9 |
9,10*,11,12*,12,14,15,16*,42*,46,49* |

4.10 |
16,17* |

5.1 |
7*,8*,30* |

5.2 |
12*,21*,28,34* |

5.3 |
4,7*,24,29*,32* |

5.4 |
21-26,30* |

5.5 |
12,17*,24,26*,39* |

5.6 |
10*,11,16* |

5.7 |
(5-16)*,39*,44* |

6.1 |
25*,26,28*,34* |

6.2 |
13*,16(c)* |

6.3 |
12,16,22*,37*,38* |

6.4 |
5,6,8*,21* |

6.5 |
9,13,14*,38*,40* |

6.6 |
15,18,20*,24,26*,31*,36* |

6.7 |
3*,4,7,8*,21*,39,40* |

6.8 |
2*,8,10*,12*,20*,33*,24,46,54* |

6.9 |
15,16,18*,22,34*,37 |

Ch .6 review |
6,8,14,30,41*,58,95,96*,109,118*,124*,145* |

7.1 | 8*,9*,11*,15* |

7.2 | 3*,8*,9*,14*,18*,31*,34* |

7.3 | 2*,4*,12*,15*,16*,19*,33*,36*,37* |

7.4 | 4*,11*,13*,16*,21*,24*,33*,36* |

7.5 | (3-8)*,20*,24*,26*,32*,49*,52*,58* |

7.6 | 3*,7*,8*,14*,20*,24*,27*,42,43,49*,52,55* |

7.7 | 1-59 (* -
multiples of 4 are for credit) |

Ch.7 review |
43-161 (* -
multiples of 5 are for credit) |